Author(s)

Leonardo Mondaini^1,2*

¹Department of Oncology, University of Alberta, Edmonton, Canada.
²Grupo de Física Teórica e Experimental, Departamento de Ciências Naturais, Universidade Federal do Estado do Rio de Janeiro, Rio de Janeiro, Brazil.

We show how the famous soliton solution of the classical sine-Gordon field theory in (1 + 1)-dimensions may be obtained as a particular case of a solution expressed in terms of the Jacobi amplitude, which is the inverse function of the incomplete elliptic integral of the first kind.

Solitons, Sine-Gordon Field Theory, Elliptic Integrals, Jacobi Amplitude

Mondaini, L. (2014) The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function. Journal of Applied Mathematics and Physics, 2, 1202-1206. doi: 10.4236/jamp.2014.213141.